In the number series 2, 6, 14, 30, 62, 126, the next term is _______. – UGC NET Question

The first-level differences are 4, 8, 16, 32 and 64. Each difference is double the previous one, representing a geometric progression at the second level. The next difference should therefore be 128. Adding 128 to the last term 126 gives 254, so 254 is the value that preserves the doubling structure among the differences.

Option A:
Option A gives 250, corresponding to a difference of 124 from 126. This breaks the exact doubling rule, since 124 is not twice 64. Therefore 250 does not respect the second-level geometric behaviour.

Option B:
Option B gives 252, implying a difference of 126, which again does not equal 2×64. This leads to an inconsistent change in the pattern of differences. Hence 252 cannot be accepted.

Option C:
Option C gives 256, corresponding to a difference of 130 from 126. That would overshoot the expected difference of 128 and disrupt the doubling rule for the gaps. Thus 256 is not a valid continuation.

Option D:
Option D gives 254, which is 128 more than 126. The differences become 4, 8, 16, 32, 64, 128, perfectly doubling each time. This strong and simple structure confirms 254 as the correct next term.